Answer:

a. New moon

A new moon is the moon when it first appears as a thin curved shape at the start of its four-week cycle. The new moon is also the time of the month when the moon appears in this way.

b. First quarter

A week after New Moon, the Moon reaches its First Quarter. In this phase, the Moon is in quadrature (elongation = 90o, position C in the diagram below), and one half of the Moon's disk is illuminated as seen from Earth. The First Quarter Moon rises at noon, transits the meridian at sunset and sets at midnight.

c. Full moon

The full moon is the lunar phase when the Moon appears fully illuminated from Earth's perspective. This occurs when Earth is located between the Sun and the Moon. This means that the lunar hemisphere facing Earth – the near side – is completely sunlit and appears as a circular disk.

d. Waxing

When the Moon is in between the Earth and the Sun, the side of the Moon facing away from the Earth is fully illuminated, and the side we can see is shrouded in darkness. As the Moon orbits the Earth, the angle between the Moon and the Sun increases. ... This is what astronomers call a waxing moon.

e. Waning

The moon is called a waning moon when it is in the phase in which its visible surface area is getting smaller. A waning moon occurs between a full moon (when the visible surface is fully round and lit up) and a new moon (when the surface that faces Earth is completely covered in shadow).